Waveguides in Microwave Engineering

**Chapter 5**

**Abstract**

Rigorous Analysis of the

Filled with Anisotropic

*Hedi Sakli and Wyssem Fathallah*

Structure Simulator (HFSS) software.

analysis, waveguides discontinuity

**1. Introduction**

**65**

Metamaterial

Propagation in Metallic Circular

Waveguide with Discontinuities

In this chapter, we present an extension of the rigorous analysis of the propagation of electromagnetic waves in magnetic transverse (TM) and transverse electric (TE) modes in a metallic circular waveguide partially filled with anisotropic metamaterial. In our analysis, the design of waveguide filters with uniaxial discontinuities is based on the determination of the higher-order modes, which have been analyzed and exploited. Below the cutoff frequency, the back backward waves can propagate in an anisotropic material. The numerical results with our MATLAB code for TM and TE modes were compared to theoretical predictions. Good agreements have been obtained. We analyzed a waveguide filters filled with partially anisotropic metamaterial using the mode matching (MM) technique based on the Scattering Matrix Approach (SMA), which, from the decomposition of the modal fields (TE and TM modes), are used to determine the dispersion matrix and thus the characterization of a discontinuity in waveguide. We extended the application of MM technique to the anisotropic material. By using modal analysis, our approach has considerably reduced the computation time compared to High Frequency

**Keywords:** anisotropic metamaterials, forward and backward waves, MM, modal

Guided modes in circular waveguides consist of metamaterials [1–13] have been studied in the literature. Many studies of propagation modes in this waveguides with isotropic media [14–17] or double negative metamaterials [18, 19] have been presented in the literature. However, the rigorous study of the dispersion of anisotropic metamaterials in circular waveguides presents a lack in the literature. In this chapter, we present an extension of the rigorous analysis of the propagation of electromagnetic waves in magnetic transverse (TM) and electric transverse (TE) modes in the case of anisotropic circular waveguides, who take account of the spatial distribution of the permittivity and permeability of the medium. In this
